Quel After I hours there are P (t) cells present in a culture, where PU) = 5000 602: . (i) How many cells were present initially? (ii) Give a differential equation satisfied byP (1') (iii) At what time will the population double? (iv) When will 20,000 cells be present? QueZ Find the present value of $1000 payable at the end of 3 years, if money may be invested at 8% with interest compounded continuously. Que3 A movie theater has a seating capacity of 3000 people. The number of people 18000 attending a show at price ,0 dollars per ticket is q = 1500. Currently, P the price is $6 per ticket. (i) Is demand elastic or inelastic at p = 6 ? (ii) If the price is lowered, will revenue increase or decrease? Que4 A soap manufacturer estimates that its marginal cost of producing soap powder is C ' (x) = 0.2x +1 hundred dollars per ton at a production level of x tons per day. Fixed costs are $200 per day. Find the cost of producing x tons of soap powder per day. Also nd the cost if production level has increased from 20 tons to 30 tons per day. QueS (i) Evaluate I[x3 + 765x + Ede x (ii) Evaluate I[x2x2 +1] dx x